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# Simple Linear Regression and Correlation 10-82 10-86 10-84

Problem 10-82

A portfolio of two independent securities is to be constructed. The mean returns of the securities are 4% and 10%. The standard deviations are 1% and 3%, respectively. Find the expected value and the standard deviation of the return from a portfolio that invests a suitable proportion in each security to ensure a portfolio return of 8%.

Problem 10-86

The following data are operating income X and monthly stock close Y for Clorox, Inc. Graph the data. Then regress log Y on X.

X (\$ millions): 240, 250, 260, 270, 280, 300, 310, 320, 330, 340, 350, 360, 370, 400, 410, 420, 430, 450

Y (\$s): 45, 42, 44, 46, 47, 50, 48, 60, 61, 59, 67, 75, 74, 85, 95, 110, 125,
130

Predict Y for X = 305.

Problem 10-84

The following data are from the Wall Street Journal. They represent the average number of times per year respondents in a national survey ate store-bought fresh fruit and fresh vegetables at home. Run a regression of one variable against the other and test for a linear relationship.

Year: 1998 1999 2000 2001 2002 2003
Avg # fruit 135 126 129 117 115 123
Avg # Veg 137 138 134 120 121 128

Problem 10-83

The following data from Fortune present the total number of cars sold per year in the US and the percentage of these cars made by GM. Run a regression of the percentage of total cars sold by GM versus total number of cars. Interpret your findings.

1954650.2 19557.850.4 19607.344.0 196510.349.9 197010.139.5 197510.843.1 198011.544.0 198515.440.1 199013.536.0 199515.531.7 200017.428.6 200517.127.8 YearTotal Cars Sold% of GM Cars

#### Solution Preview

See the attached file for complete solution. The text here may not be copied exactly as some of the symbols / tables may not print. Thanks

Statistics Problem Quote

Simple Linear Regression and Correlation

Problem 10-82

A portfolio of two independent securities is to be constructed. The mean returns of the securities are 4% and 10%. The standard deviations are 1% and 3%, respectively. Find the expected value and the standard deviation of the return from a portfolio that invests a suitable proportion in each security to ensure a portfolio return of 8%.

First, calculate the proportion of securities
Say proportions invested are x and 1-x, then we have
Expected return = x*r1+(1-x)*r2
Expected value of return on portfolio = 8%
r1=4% r2=10%
So we have 8%=x*4%+(1-x)*10%
x=1/3 and 1-x=2/3 so invest 1/3 in first security and two third in second security.
Now to ...

#### Solution Summary

Answers four problems on linear regression and correlation. This post provides a good practice to understand the concepts of linear regression and correlation.

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